Mathematics 134 – Intensive Calculus for Science 2 Exam 1 – Things To Know February 12, 2000

General Information

As announced in the course syllabus, the first full-period midterm exam of the semester will be given in class on Friday, February 16. The format will be similar to that of the midterm exams last semester. The exam will cover the material since the start of the semester (Quizzes 1,2,3), including the following material from Chapter 3 sections 4, Chapter 6 sections 1,2,3, and Chapter 7 sections 1,2,3,4 of the text:

1) The Fundamental Theorem of Calculus: If F (x) is an antiderivative of a continuous function f(x) on [a, b], then

∫_{a}^{b} f(x) dx = F (b) − F (a)

2) Antiderivatives graphically and numerically

3) The power, sum, and constant multiple rules for antiderivatives

4) Differential equations \frac{dy}{dx} = f(x)

5) Indefinite integrals by substitution

6) Integration by parts

7) Using the table of integrals

There will be a review for the exam in class on Thursday, February 15. I will also set up an evening session with Jodi Marani on Thursday for other questions.

Sample Exam

I. The following graph shows y = F′(x), the derivative of F. Sketch the graphs y = F (x) in the cases F (0) = 0 and F (0) = 1.

II. A child throws a baseball vertically upward with velocity 12 ft/sec from an initial height of 4 feet. The acceleration of the baseball due to gravity is -32 ft/sec^{2}. A) Make a table showing the velocity of the baseball at 1/8 second intervals for t = 0 to

t = 1. B) When does the baseball reach its highest point? When does it hit the ground? C) Find the greatest height the ball reaches.

III. Compute the following integrals. Say which method you are using for each. If you use an entry from the table of integrals, say which one.

A) ∫ 5x^{4} − 3\sqrt{x} + e^{x} dx

B) ∫ x(4x^{2} − 3)^{3/5} dx C) ∫_{1}^{2} sin^{2}(πx) cos(πx) dx D) ∫ x^{2}e^{4x} dx

E) ∫ \frac{dx}{\sqrt{1−9x^{2}}}

F) ∫ e^{3x} cos(4x) dx

Also see Problem Sets 1,2,3, the last three quizzes, and the Review Problems from the ends of Chapters 3,6,7 in the text for other practice problems.